Multiplication and Division, Part 1

Lesson 7

Math

Unit 2

3rd Grade

Lesson 7 of 21

Objective


Demonstrate the commutativity of multiplication.

Common Core Standards


Core Standards

  • 3.OA.B.5 — Apply properties of operations as strategies to multiply and divide. Students need not use formal terms for these properties. Example: Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56. (Distributive property.) Example: If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known (Commutative property of multiplication.) 3 × 5 × 2 can be found by 3 × 5 = 15, then 15 × 2 = 30, or by 5 × 2 = 10, then 3 × 10 = 30. (Associative property of multiplication.)

Foundational Standards

  • 2.NBT.A.2
  • 2.OA.C.3
  • 2.OA.C.4

Criteria for Success


  1. Understand that a column is a vertical group in an array. 
  2. Understand that when multiplying numbers, the order in which factors are multiplied doesn’t matter (MP.7). 
  3. Demonstrate and explain the commutativity of multiplication using models (MP.3). 
  4. Use the commutative property to switch the order of factors in order to find products (e.g., $$5\times8$$ becomes $$8\times5$$ so that students can count by fives, the size of each group).

Tips for Teachers


Students need not use formal terms for the properties of operations, including the terms "commutative" or "commutative property." However, exposure to the term is helpful so that students can develop and use a common language and thus is introduced in this lesson. 

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Anchor Tasks


Problem 1

a.   Mr. Barron is working with a small group of students. He sets up their seats facing the whiteboard into three rows with four chairs in each row.

  1. Draw the seats in Mr. Barron’s room below, using squares to represent the seats.

  1. Write a multiplication equation that represents the total number of seats facing the whiteboard.

b.   Sometimes Mr. Barron wants to use chart paper on the side of his room, which you can see in the diagram above. Imagine students facing Mr. Barron at the chart paper.

Write a multiplication equation that represents the total number of seats facing the chart paper. 

c.   What do you notice about the equations you wrote in Parts (a) and (b)? What do you wonder?

Guiding Questions

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Problem 2

Is the following equation true or false? Explain your answer. 

$$2 \times 5 = 5\times 2$$

Guiding Questions

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Problem 3

Solve. 

a.    $$2\times 8 = $$ _____

b.     _____ $$= 5\times 6$$

c.    _____ $$= 10\times 7$$

Guiding Questions

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Problem Set


Answer Keys

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Discussion of Problem Set

  • We don’t know our 3 or our 6 count-bys yet. How were you able to solve #1? 
  • Do you agree or disagree with Ms. Nenadal’s equation? How did an array help you to demonstrate your thinking? 
  • How did the commutative property help you to solve in #7? 
  • Are there other operations besides multiplication where you can switch the order of the numbers without having an effect on the solution? Which ones?

Target Task


Is the following equation true or false? Show or explain your thinking. 

$$3\times5=5\times3$$

Student Response

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Additional Practice


The Extra Practice Problems can be used as additional practice for homework, during an intervention block, etc. Daily Word Problems and Fluency Activities are aligned to the content of the unit but not necessarily to the lesson objective, therefore feel free to use them anytime during your school day.

Extra Practice Problems

Answer Keys

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Word Problems and Fluency Activities

Word Problems and Fluency Activities

Help students strengthen their application and fluency skills with daily word problem practice and content-aligned fluency activities.

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Lesson 6

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Lesson 8

Lesson Map

A7CB09C2-D12F-4F55-80DB-37298FF0A765

Topic A: The Meaning of Multiplication and Division

Topic B: Multiplication and Division by 2, 5, and 10

Topic C: Multiplication and Division by 3 and 4

Topic D: More Complex Multiplication and Division Problems

Topic E: Scaled Picture and Bar Graphs

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